How do I calculate sample size for a survey?

Pick the confidence level, margin of error, and expected proportion p. Use n0 = z²·p·(1−p)/e². If your population is finite, apply n = n0 / (1 + (n0 − 1)/N).

What is a good default proportion?

Use p = 0.5 when you don't know the true proportion: this gives the largest (most conservative) sample size.

What if I have a small population?

When your sample is a large fraction of the total population, use the finite population correction (FPC) to reduce the required sample size. This tool does it automatically when you enter N.

Sample Size Calculator

Determine how many responses you need for your survey or experiment. This tool supports: proportion-based surveys (the classic approach), mean/continuous outcomes, and finite population correction when your audience is not huge.

Confidence level

choose the confidence for your estimates

Margin of error (E)

0.05 → ±5 percentage points

Expected proportion (p)

0.5 → most conservative

Population size (N)

apply FPC if filled

Initial sample size (n₀)

—

ignoring finite population

Adjusted sample size (n)

—

with FPC if N provided

z-score used

—

Sample size formulas

Survey / proportion:

\( n_0 = \frac{z^2 \, p (1 - p)}{E^2} \)

FPC: \( n = \frac{n_0}{1 + \frac{n_0 - 1}{N}} \)

Mean / continuous:

\( n_0 = \left( \frac{z \sigma}{E} \right)^2 \)

What should I enter as p?

If you do not have a previous study or pilot, use 0.5. That produces the largest required sample size and is safe.

Quick reference

Confidence	z-score	Typical MoE
90%	1.645	±5%
95%	1.96	±5%
99%	2.576	±3%

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

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Formula (extracted text)

Survey / proportion: \( n_0 = \frac{z^2 \, p (1 - p)}{E^2} \) FPC: \( n = \frac{n_0}{1 + \frac{n_0 - 1}{N}} \) Mean / continuous: \( n_0 = \left( \frac{z \sigma}{E} \right)^2 \)

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
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